9.6: Fruit Confusion

Look at the picture of the bananas and the information about the price of bananas below. Can you figure out how much just one banana would cost? In this concept, we will use proportions and logical reasoning to determine the cost of individual items given information about multiples of those items.

Guidance

In order to answer a question about the cost of an item like the one above, we can use the problem solving steps to help.

First,
describe
what you know. What do we know about the weight of the fruit? What do we know about the cost of the fruit?

Second, identify what
your job
is. In these problems, your job will be to figure out the cost or weight of one piece/pound of fruit. Or, it might be to figure out how many pieces of fruit are in a closed box.

Third, make a
plan
. In these problems, your plan should be to write a proportion that relates the weight of the fruit to the cost. Solve the proportion and use logical reasoning to answer the question that was asked.

Fourth,
solve
. Implement your plan.

Fifth,
check
. Check your answer by verifying that it works with all of the original information.

Example A

Look at the pictures below and answer the question.

Solution:

We can use problem solving steps to help us.

Example B

Look at the pictures below and answer the question.

Solution:

We can use problem solving steps to help us.

Example C

Look at the pictures below and answer the question.

Solution:

We can use problem solving steps to help us.

Concept Problem Revisited

We can use problem solving steps to help us.

Vocabulary

A
proportion
is an equation that states that two ratios are equal. In this concept, we can use
proportions
because the ratio of weight to cost is constant for each type of fruit. As long as we know the cost of fruit for a particular weight of that fruit, we can find the cost of that fruit for any weight of that fruit using
proportions.

Guided Practice

1.

2.

3.

Answers:

1.
, so
, and
.

2.
, so
is
, and
is 10.

3.
, so
, and

Practice

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Description

In this concept, students use proportions and logical reasoning to answer questions about the cost and weight of fruit.

Learning Objectives

Students use proportions and logical reasoning to answer questions about the cost and weight of fruit. Students use problem solving steps to help.